No, this song has nothing to do with Sting of The Police. In fact, it couldn't sound any less similar.
The Neighbourhood have been sporadically releasing new singles over the course of the last few months in support of their touring. Each single is matched by an accompanying song from another band -- with past participants including The 1975. Check out "No Grey" and "West Coast" for prior examples.
"$TING" is typically groovy and downtempo, fully aligned with the band's signature sound. Definitely adding this one to my favorites.